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CBSE · Class 7 · Mathematics

Geometric Twins

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
In △PQR and △MKL, PQ = MK, QR = KL and RP = LM. The triangles are congruent by:
  1. SSS
  2. RHS
  3. ASA
  4. SAS
2.
△GHI ≅ △WUV. Which side equals HI?
  1. IG
  2. WU
  3. UV
  4. VW
3.
Two figures that have exactly the same shape and size are called:
  1. parallel
  2. symmetrical
  3. similar only
  4. congruent
4.
△UVW ≅ △CBA. Which angle equals ∠V?
  1. ∠W
  2. ∠A
  3. ∠B
  4. ∠C
5.
△KLM ≅ △TSR. ∠K = 62° and ∠L = 29°. What is ∠R?
  1. 118°
  2. 62°
  3. 89°
  4. 29°
6.
△LMN has sides of 7 cm, 10 cm, 6 cm. If △LMN ≅ △CBA, the perimeter of △CBA is:
  1. 23 cm
  2. 24 cm
  3. 46 cm
  4. 16 cm
7.
AB = PQ, BC = QR and CA = RP. The triangles are congruent by:
  1. ASA
  2. SAS
  3. SSS
  4. RHS
8.
In △GHI, GH = GI and ∠H = 62°. What is ∠G?
  1. 118°
  2. 62°
  3. 56°
  4. 124°
Section B — Short answer8 × 2 = 16 marks
9.
△GHI ≅ △VWU. GH = 11 cm, HI = 7 cm and IG = 11 cm. Find VW, WU and UV.
10.
In △UVW, UV = 12 cm, ∠V = 46° and VW = 6 cm. In △ABC, AB = 12 cm, ∠B = 46° and BC = 6 cm. Are they congruent? By which rule? Write the congruence.
11.
△ABC ≅ △RQP. In △RQP, ∠R = 84° and ∠Q = 50°. Find all three angles of △ABC.
12.
One triangle has sides 5, 10, 9 cm and another has sides 9, 10, 6 cm. Are they congruent?
13.
△LMN and △UVW both have a right angle. Each has a hypotenuse of 30 cm and one other side of 18 cm. Are they congruent? By which rule?
14.
Two equilateral triangles each have a perimeter of 45 cm. What is the length of each side, what is each angle, and are the triangles congruent?
15.
In kite ABCD, AB = AD = 7 cm and CB = CD = 12 cm. ∠BAC = 47°. Find ∠DAC and give the reason.
16.
A rectangle 12 cm by 3 cm is cut along a diagonal. Are the two triangles congruent? What is the area of each?
Section C — Word problems4 × 4 = 16 marks
17.
Two roof trusses are congruent triangles. One has a base of 4 m, a height of 3 m and an angle of 120° at the top. What are the base, height and top angle of the other truss?
18.
A bridge has two triangular supports. In each, one side is 10 m and the angles at the ends of that side are 78° and 88°. Are the supports congruent, and by which rule? What is the third angle of each?
19.
Arjun folds a rectangular sheet 22 cm by 19 cm along its diagonal. Do the two halves fit exactly on each other? What is the area of each half?
20.
A kite frame has AB = AD = 32 cm and CB = CD = 53 cm, with a stick along AC. The angle between AB and the stick is 69°. What is the angle between AD and the stick? Which rule shows the two halves are congruent?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 7 · Mathematics

Answer key

Geometric Twins · AW-7M-CNG-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(a) SSS—
2(c) UVthe letters match in order
3(d) congruent—
4(c) ∠Bthe letters match in order
5(c) 89°∠R = ∠M = 180° − 62° − 29°
6(a) 23 cmcongruent triangles have equal sides, so equal perimeters
7(c) SSS—
8(c) 56°∠I = ∠H = 62°; 180° − 2 × 62°
911 cm, 7 cm, 11 cmmatching sides of congruent triangles are equal
10Yes, by SAS; △UVW ≅ △ABCtwo sides and the angle between them are equal
11∠A = 84°, ∠B = 50°, ∠C = 46°matching angles are equal; the third is 180° − 134°
12Nothe side lengths are not all the same
13Yes, by RHSright angle, equal hypotenuses and one equal side
1415 cm; 60°; yes45 ÷ 3 = 15; all sides equal, so SSS
1547°△ABC ≅ △ADC by SSS (AC is shared), so the matching angles are equal
16Yes; 18 cm2SSS: the same three sides; 12 × 3 ÷ 2
174 m, 3 m, 120°congruent shapes have all matching parts equal
18Yes, by ASA; 14°180° − 78° − 88°
19Yes, they are congruent; 209 cm222 × 19 = 418; half is 209
2069°; SSSAB = AD, CB = CD and AC is shared